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II-A 7.26 b

Picture of Arjun Suryawanshi
II-A 7.26 b
by Arjun Suryawanshi - Sunday, January 31, 2021, 11:45 AM

I am missing something for my combinatorial proof. So far, I am able to show how to get 2*a_(n-1), and that we have to add 1 to that because we didn't take into account just inviting the nth friend, but I don't see where the remaining missing 1 is. Right now, my proof is stuck at 2*a_(n-1) + 1.

Picture of Areteem Professor
Re: II-A 7.26 b
by Areteem Professor - Monday, February 1, 2021, 2:50 PM

Hint: note that $a_{n-1}$ does not include the case "invite all the $n-1$ friends", but when you have $n$ friends to choose from, this should be possible as well.